Data.Monoid.Inf

Make semigroups under min or max into monoids by adjoining an element corresponding to infinity (positive or negative, respectively). These types are similar to Maybe (Min a) and Maybe (Max a) respectively, except that the Ord instance matches the Monoid instance.

Documentation

data Inf p a

Inf p a represents the type a extended with a new "infinite" value, which is treated as either positive or negative infinity depending on the type index p. This type exists mostly for its Ord, Semigroup, and Monoid instances.

Constructors

Infinity

Finite a

Instances

Foldable (Inf p)

Defined in Data.Monoid.Inf

Methods

fold :: Monoid m => Inf p m -> m

foldMap :: Monoid m => (a -> m) -> Inf p a -> m

foldMap' :: Monoid m => (a -> m) -> Inf p a -> m

foldr :: (a -> b -> b) -> b -> Inf p a -> b

foldr' :: (a -> b -> b) -> b -> Inf p a -> b

foldl :: (b -> a -> b) -> b -> Inf p a -> b

foldl' :: (b -> a -> b) -> b -> Inf p a -> b

foldr1 :: (a -> a -> a) -> Inf p a -> a

foldl1 :: (a -> a -> a) -> Inf p a -> a

toList :: Inf p a -> [a]

null :: Inf p a -> Bool

length :: Inf p a -> Int

elem :: Eq a => a -> Inf p a -> Bool

maximum :: Ord a => Inf p a -> a

minimum :: Ord a => Inf p a -> a

sum :: Num a => Inf p a -> a

product :: Num a => Inf p a -> a

Traversable (Inf p)

Defined in Data.Monoid.Inf

Methods

traverse :: Applicative f => (a -> f b) -> Inf p a -> f (Inf p b)

sequenceA :: Applicative f => Inf p (f a) -> f (Inf p a)

mapM :: Monad m => (a -> m b) -> Inf p a -> m (Inf p b)

sequence :: Monad m => Inf p (m a) -> m (Inf p a)

Applicative (Inf p)

Defined in Data.Monoid.Inf

Methods

pure :: a -> Inf p a

(<*>) :: Inf p (a -> b) -> Inf p a -> Inf p b

liftA2 :: (a -> b -> c) -> Inf p a -> Inf p b -> Inf p c

(*>) :: Inf p a -> Inf p b -> Inf p b

(<*) :: Inf p a -> Inf p b -> Inf p a

Functor (Inf p)

Defined in Data.Monoid.Inf

Methods

fmap :: (a -> b) -> Inf p a -> Inf p b

(<$) :: a -> Inf p b -> Inf p a

Monad (Inf p)

Defined in Data.Monoid.Inf

Methods

(>>=) :: Inf p a -> (a -> Inf p b) -> Inf p b

(>>) :: Inf p a -> Inf p b -> Inf p b

return :: a -> Inf p a

Bounded a => Bounded (NegInf a)

Defined in Data.Monoid.Inf

Methods

minBound :: NegInf a

maxBound :: NegInf a

Bounded a => Bounded (PosInf a)

Defined in Data.Monoid.Inf

Methods

minBound :: PosInf a

maxBound :: PosInf a

(Data p, Data a) => Data (Inf p a)

Defined in Data.Monoid.Inf

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Inf p a -> c (Inf p a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Inf p a)

toConstr :: Inf p a -> Constr

dataTypeOf :: Inf p a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Inf p a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Inf p a))

gmapT :: (forall b. Data b => b -> b) -> Inf p a -> Inf p a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Inf p a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Inf p a -> r

gmapQ :: (forall d. Data d => d -> u) -> Inf p a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Inf p a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Inf p a -> m (Inf p a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Inf p a -> m (Inf p a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Inf p a -> m (Inf p a)

Ord a => Monoid (Inf Neg a)

An ordered type extended with negative infinity is a monoid under max, with negative infinity as the identity element.

Defined in Data.Monoid.Inf

Methods

mempty :: Inf Neg a

mappend :: Inf Neg a -> Inf Neg a -> Inf Neg a

mconcat :: [Inf Neg a] -> Inf Neg a

Ord a => Monoid (Inf Pos a)

An ordered type extended with positive infinity is a monoid under min, with positive infinity as the identity element.

Defined in Data.Monoid.Inf

Methods

mempty :: Inf Pos a

mappend :: Inf Pos a -> Inf Pos a -> Inf Pos a

mconcat :: [Inf Pos a] -> Inf Pos a

Ord a => Semigroup (Inf Neg a)

An ordered type extended with negative infinity is a semigroup under max.

Defined in Data.Monoid.Inf

Methods

(<>) :: Inf Neg a -> Inf Neg a -> Inf Neg a

sconcat :: NonEmpty (Inf Neg a) -> Inf Neg a

stimes :: Integral b => b -> Inf Neg a -> Inf Neg a

Ord a => Semigroup (Inf Pos a)

An ordered type extended with positive infinity is a semigroup under min.

Defined in Data.Monoid.Inf

Methods

(<>) :: Inf Pos a -> Inf Pos a -> Inf Pos a

sconcat :: NonEmpty (Inf Pos a) -> Inf Pos a

stimes :: Integral b => b -> Inf Pos a -> Inf Pos a

Read a => Read (Inf p a)

Defined in Data.Monoid.Inf

Methods

readsPrec :: Int -> ReadS (Inf p a)

readList :: ReadS [Inf p a]

readPrec :: ReadPrec (Inf p a)

readListPrec :: ReadPrec [Inf p a]

Show a => Show (Inf p a)

Defined in Data.Monoid.Inf

Methods

showsPrec :: Int -> Inf p a -> ShowS

show :: Inf p a -> String

showList :: [Inf p a] -> ShowS

Eq a => Eq (Inf p a)

Defined in Data.Monoid.Inf

Methods

(==) :: Inf p a -> Inf p a -> Bool

(/=) :: Inf p a -> Inf p a -> Bool

Ord a => Ord (Inf Neg a)

Negative infinity is less than any finite value.

Defined in Data.Monoid.Inf

Methods

compare :: Inf Neg a -> Inf Neg a -> Ordering

(<) :: Inf Neg a -> Inf Neg a -> Bool

(<=) :: Inf Neg a -> Inf Neg a -> Bool

(>) :: Inf Neg a -> Inf Neg a -> Bool

(>=) :: Inf Neg a -> Inf Neg a -> Bool

max :: Inf Neg a -> Inf Neg a -> Inf Neg a

min :: Inf Neg a -> Inf Neg a -> Inf Neg a

Ord a => Ord (Inf Pos a)

Positive infinity is greater than any finite value.

Defined in Data.Monoid.Inf

Methods

compare :: Inf Pos a -> Inf Pos a -> Ordering

(<) :: Inf Pos a -> Inf Pos a -> Bool

(<=) :: Inf Pos a -> Inf Pos a -> Bool

(>) :: Inf Pos a -> Inf Pos a -> Bool

(>=) :: Inf Pos a -> Inf Pos a -> Bool

max :: Inf Pos a -> Inf Pos a -> Inf Pos a

min :: Inf Pos a -> Inf Pos a -> Inf Pos a

data Pos

Type index indicating positive infinity.

Instances

Bounded a => Bounded (PosInf a)

Defined in Data.Monoid.Inf

Methods

minBound :: PosInf a

maxBound :: PosInf a

Ord a => Monoid (Inf Pos a)

An ordered type extended with positive infinity is a monoid under min, with positive infinity as the identity element.

Defined in Data.Monoid.Inf

Methods

mempty :: Inf Pos a

mappend :: Inf Pos a -> Inf Pos a -> Inf Pos a

mconcat :: [Inf Pos a] -> Inf Pos a

Ord a => Semigroup (Inf Pos a)

An ordered type extended with positive infinity is a semigroup under min.

Defined in Data.Monoid.Inf

Methods

(<>) :: Inf Pos a -> Inf Pos a -> Inf Pos a

sconcat :: NonEmpty (Inf Pos a) -> Inf Pos a

stimes :: Integral b => b -> Inf Pos a -> Inf Pos a

Ord a => Ord (Inf Pos a)

Positive infinity is greater than any finite value.

Defined in Data.Monoid.Inf

Methods

compare :: Inf Pos a -> Inf Pos a -> Ordering

(<) :: Inf Pos a -> Inf Pos a -> Bool

(<=) :: Inf Pos a -> Inf Pos a -> Bool

(>) :: Inf Pos a -> Inf Pos a -> Bool

(>=) :: Inf Pos a -> Inf Pos a -> Bool

max :: Inf Pos a -> Inf Pos a -> Inf Pos a

min :: Inf Pos a -> Inf Pos a -> Inf Pos a

data Neg

Type index indicating negative infinity.

Instances

Bounded a => Bounded (NegInf a)

Defined in Data.Monoid.Inf

Methods

minBound :: NegInf a

maxBound :: NegInf a

Ord a => Monoid (Inf Neg a)

An ordered type extended with negative infinity is a monoid under max, with negative infinity as the identity element.

Defined in Data.Monoid.Inf

Methods

mempty :: Inf Neg a

mappend :: Inf Neg a -> Inf Neg a -> Inf Neg a

mconcat :: [Inf Neg a] -> Inf Neg a

Ord a => Semigroup (Inf Neg a)

An ordered type extended with negative infinity is a semigroup under max.

Defined in Data.Monoid.Inf

Methods

(<>) :: Inf Neg a -> Inf Neg a -> Inf Neg a

sconcat :: NonEmpty (Inf Neg a) -> Inf Neg a

stimes :: Integral b => b -> Inf Neg a -> Inf Neg a

Ord a => Ord (Inf Neg a)

Negative infinity is less than any finite value.

Defined in Data.Monoid.Inf

Methods

compare :: Inf Neg a -> Inf Neg a -> Ordering

(<) :: Inf Neg a -> Inf Neg a -> Bool

(<=) :: Inf Neg a -> Inf Neg a -> Bool

(>) :: Inf Neg a -> Inf Neg a -> Bool

(>=) :: Inf Neg a -> Inf Neg a -> Bool

max :: Inf Neg a -> Inf Neg a -> Inf Neg a

min :: Inf Neg a -> Inf Neg a -> Inf Neg a

type PosInf a = Inf Pos a

The type a extended with positive infinity.

type NegInf a = Inf Neg a

The type a extended with negative infinity.

minimum :: Ord a => [a] -> PosInf a

Find the minimum of a list of values. Returns positive infinity iff the list is empty.

maximum :: Ord a => [a] -> NegInf a

Find the maximum of a list of values. Returns negative infinity iff the list is empty.

Type-restricted constructors

posInfty :: PosInf a

Positive infinity.

negInfty :: NegInf a

Negative infinity.

posFinite :: a -> PosInf a

Embed a finite value into the space of such values extended with positive infinity.

negFinite :: a -> NegInf a

Embed a finite value into the space of such values extended with negative infinity.